A travelling locus of a vehicle mounting an on-vehicle unit which includes a Global Positioning System (GPS) is prehensible based on a set of position information such as latitude, longitude, and the like measured by the GPS.
However, an interval of an observation point of the position information by the GPS may not be sufficient with respect to desired precision of the travelling locus. Conventionally, interpolation points concerning the traveling locus are acquired by a spline interpolation method. In the spline interpolation method, when a set of points is given, a polynominal equation passing all points is acquired, and the interpolation points are obtained.
FIG. 1 is a diagram illustrating an example of interpolation points acquired by the spline interpolation method. In FIG. 1, a white dot indicates the observation point, and a black dot indicates an interpolation point. In the spline interpolation method, the polynominal equation acquired based on the set of observation points is calculated. Thus, the interpolation points are obtained on a spline curve line depicted by the polynominal equation.
Movement of the vehicle includes concepts of time and speed as well as a location. In the spline interpolation method, the time and the speed are abstracted. In a point in which the time and the speed are not considered, accuracy of the observation point acquired by the spline interpolation method may not be sufficient.